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\title{Organized SPM Results}

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\maketitle

\section{Drawbacks mentioned more than once}

    \textcolor{red}{
    \begin{enumerate}
    \item Few comparison. Sightly improvement.
    \item Why using Geodesic path?
    \item Why using "EXT" and "WID" used in Algorithm 1?
    \item The chosen of parameter alpha?
    \item The set of candidates is not the superset.
    \item What is globally optimized?
    \item How to guarantee the quad layout?
    \item Removing duplicated safety turning areas is naive and the result is wrong (more than 50\%)?
    \item The explanation of safety turning area?
    \item How and why to relax the energy constraints?
    \item Running Time?
    \item Input is uncorrect? some requirements?
    \end{enumerate}
    }

\section{Reviewer A}

    Optimization problem is briefly stated as : \\\\
    \emph{\textcolor{blue}{Choose the subset of the set of all pairwise port connections which forms a quad layout and minimizes a certain cost function.}}
    \\\\
    Main Problem:\\\\
    \emph{\textcolor{red}{The alternative strategy wrt. Tarini is insufficiently motivated and evaluated.}}

\subsection{Technique Problems}

    \begin{itemize}
    \item \textcolor{red}{Only one comparison.}
        The set of separatries does not seem to be a \textcolor{blue}{superset} of the set of connections that the local operators of Tarini et al.
        It is neither theoretically clear nor \textcolor{blue}{intuitively obvious that the proposed method produces better results (only a single comparison)}.
    
    \item \textcolor{red}{Should pay more attention to the paper of Tarini et al in the related works.}
        This is particularly critical because \textcolor{blue}{the paper cannot be understood without having read the paper of Tarini et al}.
        For instance the authors never explain \textcolor{blue}{why they take a quad mesh as input.}
        The motivation for this remains unclear (unless one reads the explanation
        in Tarini et al.). Also, \textcolor{blue}{no information about the requirements or
        expectations on the input quad meshes is provided.} What kind of quad mesh
        should it be? How can one expect the irregular vertices of the input quad
        mesh to be suitable nodes for a coarse quad patch layout? Why not take a
        triangle mesh plus some irregular layout node positions as input?
    
    \item \textcolor{red}{Not clearly define the problem ``global optimal solution"}.
        In no sense is it (as one might think from 
        the wording in abstract and introduction) the solution to the problem of
        finding the optimal quad patch layout for a given object, or to the problem
        of finding the optimal quad patch layout with the prescribed set of
        irregular vertices. The problem tackled actually is the formation of a
        layout from a somehow prescribed set of possile layout edges for a fixed
        set of irregular vertices. For this restricted problem the optimal solution
        is found with exponential time complexity.
    
    \item \textcolor{red}{The choice of the heuristic based on "safety turning areas" is not explained in detail.}
        The authors argue that short separatrices are to be
        preferred, hence a local region growing based approach is used to select
        port pairs. So far this is plausible. \textcolor{blue}{But why is it reasonable to restrict
        these connections to completely regular regions of the mesh?}
    \end{itemize}

\subsection{Unclear Terminologies}

    \begin{itemize}
    \item The terms "monotone", "separatrix", "patch layout", "well-shaped", "port"
        are used multiple times in abstract and introduction \textcolor{blue}{without being defined
        until page 3 or 4 (or not at all)}.

    \item \textcolor{blue}{How to define "well-shaped"?}

    \item The terms "patch layout", "base complex", "global structure", "connectivity graph" are \textcolor{blue}{used
        for one and the same concept}.

    \item In the introduction it remains unclear \textcolor{blue}{how Fig. 1a is obtained and what it shows} (the reader learns about this only later on page 3).

    \item why is \textcolor{blue}{"short"} always written in quotes?

    \item "methods for extracting THE quad patch layout of a quad mesh", \textcolor{blue}{"THE" seems wrong and "EXTRACTING" is unfit.}

    \item Almost all methods cited in section "Mesh segmentation" do operate on
        triangle meshes, \textcolor{blue}{not quad meshes as announced in the intro} of section 1.1.

    \item "methods based on mesh segmentation might change the number and
        distribution of the irregular vertices": this seems wrong: all methods
        except [6,11] do not take irregular vertices as input, hence they cannot
        change them. \textcolor{blue}{[6,11] keep the irregular vertices of the input.}

    \item on pages 4 and 5 suddenly a \textcolor{blue}{"cross field"} appears, which has never been
        introduced and is not explained.

    \item "mostly maintained the consistency of the irregular vertices":
        \textcolor{blue}{consistency of irregular vertices is not defined} and it remains unclear why
        only \textcolor{blue}{"mostly"}.

    \item "they are either {u,-u}": \textcolor{blue}{why can the sign change}? Shouldn't it be always
        u or always -u?

    \item \textcolor{blue}{separatrices definition changed.} In section 2 separatrices are defined as edge sequences, later they are
        geodesic paths across the faces.

    \item why are the edges in the edge sequences \textcolor{blue}{directed}?

    \item "four types of safety turning areas": \textcolor{blue}{There are only two, and these are
        symmetric} (a property that could be exploited to simplify Algorithm 1,
        which is quite repetitive in its current formulation).

    \item on page 4 left the definition of \textcolor{blue}{Lwid and Lext} seems to be confused.

    \item it remains unclear why the method deals partly with edge sequences and
        partly with geodesics. \textcolor{blue}{Why not measure the actual length of the geodesic}
        and use that in the optimization instead of the naive Lwid+Lext+2?

    \item "using geodesic path, instead of edge sequence to analyze the topology of
        path layout is robust and efficiently": what does robust and efficient mean
        here? \textcolor{blue}{No method to analyze the topology} based on edge sequences was
        provided, so \textcolor{blue}{no statement about relative robustness and efficiency} can be
        made here.

    \item it remains unclear \textcolor{blue}{why an "energy constraint" is added} (page 6 right
        bottom). The authors say that non-quad solutions are excluded iteratively
        (probably using constraints that forbid one specific solution), so why does
        one additionally add this energy constraint in order to find other
        solutions until one is quad-only?

    \item what does it mean in detail to \textcolor{blue}{"relax" the energy constraint}?

    \item \textcolor{blue}{the choice of parameter alpha} is never addressed.

    \item how can the removal of duplicates reduce the number of candidate
        separatrices by \textcolor{blue}{more than 50\%} (cf. Table 1)?

    \item \textcolor{blue}{the contributions list is rather confuse and mixes in technical
        explanations.}
    \end{itemize}

\subsection{English Grammar Errors}

    \begin{itemize}
    \item "each solution is detected whether to extract quad patch layout"

    \item "finally make the mesh possess, as much as possible."

    \item "operations were high coupling with the energy"

    \item "makes the separatrices in the safety turning area along the local direction of the cross field"
    \end{itemize}

\section{Reviewer B}

    At the moment, has strong technical weaknesses, e.g. the method does not
    take into account \textcolor{red}{feature properties} of the surface. This is due to the
    very essence of the algorithm which only aims at shortest connections.

\subsection{Technique Problems}

    \begin{itemize}
    \item What happens if the base complex of the quadrilateral is \textcolor{blue}{already
        optimal} in the sense of frame alignment and number of patches?

    \item \textcolor{blue}{Why would someone choose to implement this method rather than the one of
        Tarini et al.?} (If at the end it turns out to be slow anyway).
        
    \item In this regards, it would be nice to see \textcolor{blue}{some running time benchmarks}.

    \item In the formulation, the parameter alpha appears. \textcolor{blue}{How do the results
        depend on alpha}?
    
    \item \textcolor{blue}{Does the all quads solution always exist}? if yes: is there a guarantee
        for that?
        
    \item The intended \textcolor{blue}{NURBS fitting} mentioned in the abstract is not investigated in detail.
    
    \item Figure 5 seems wrong: \textcolor{blue}{singularities have valence 4 in this illustration}.
        The same as Figure 7.
        
    \item There are some problems with Figure 11 a2. Why is it not the same as
        Figure 2d? \textcolor{blue}{is it all quads?}
        
    \item \textcolor{blue}{Why do the separatrices look only tangential at the singularity and
        suddenly deviate?} (I guess its because of the geodesics)
    \end{itemize}

\section{Reviewer C}

    There is no guarantee that the algorithm will eventually \textcolor{red}{return a quad
    layout}, not to mention the unpredictable, possibly enormous \textcolor{red}{running time}
    even if a result is returned.

\subsection{Technique Problems}

    \begin{itemize}
    \item \textcolor{blue}{While geodesic paths are used to check quad topology, it is not clear
        which path (geodesic or separatrix) is used in the final result.} If former,
        the shape of the path is sub-optimal. If latter, the layout boundaries will
        self-intersect.

    \item \textcolor{blue}{Why the result is global optimal?}
        The authors claim that their optimization gives "globally optimal
        solution", which I can't see why. In particular, the relaxation of energy
        constraint is never explained, and I can't see how the relaxation can be
        done in a way to not to miss a possible solution.

    \item The algorithm's \textcolor{blue}{results highly depend on the quality of the input quad
        mesh}. There is no mentioning of what method was used to generate the input,
        and no evaluation of how the algorithm is affected by the quality of the
        input quad mesh.

    \item \textcolor{blue}{The result of method seems sub-optimal compared to recent methods}, such as
        [16]. Also, the English language of the text needs substantial improvement.

    \item when explaining the left/right of safety turning area (Page 4), the area
        in \textcolor{blue}{Fig 4(b)} is still at "left" part of the x-did of port $e_3^0$?
        
    \item \textcolor{blue}{Fig 8 is confusing}, and (a)(b)(c) seems to talk about the same content of
        Fig 7.
        
    \item \textcolor{blue}{Need to be better explain WID and EXT.}
        In algorithm 1, "The set of all safety turning area S" should be in the
        Output. And since WID and EXT are important and "should be carefully
        chosen", it will be better to explain how those values are chosen in the
        experiment.
        
    \item \textcolor{blue}{Removing duplicated safety turning areas (Table 1 and the paragraph
        bellow) seems to be a  trivial engineering technique.} I don't see the
        necessity of explaining it in detail.
    \end{itemize}

\section{Reviewer D}

    The paper presents an alternative approach to the problem of
        generation of coarse quad layouts that performs \textcolor{red}{slightly} better than
        existing methods and it is based on integer optimization instead of a
        greedy exploration of an exponential space. The paper is very difficult to
        read, mainly due to \textcolor{red}{English errors and lack of details}.

\subsection{Unclear Terminologies}
    
    \begin{itemize}
    \item \textcolor{blue}{Explain safety turning area}.
        the section about safety turning areas is very difficult to read and
        should be expanded. The two paragraphs before equation 2 are completely
        obscure to me.
        
    \item \textcolor{blue}{The claims about optimality of the proposed approach should be strongly
        toned down}: In Algorithm 1 there is a parameter to fix the max side length
        for the turning areas and if this parameter is not set to infinity the
        method will not find an optimal solution. Probably setting infinity will
        make the algorithm too slow to be practical. Also, how do you relax the
        energy to find additional solution if they are not feasible? Are you
        guaranteed to find an optimal solution in this case?
        
    \item \textcolor{blue}{The discussion about the geodesic path is unclear.} Is it an
        approximation? If it is then the method is clearly not optimal. Please give
        more details.
        
    \item \textcolor{blue}{A few additional comparisons} with existing methods would make the paper
        stronger.
        
    \item \textcolor{blue}{deduce vs. reduce?}
    
    \item I don't understand \textcolor{blue}{figure 4}, please define the notation $e_0^0$
    
    \item \textcolor{blue}{Theory 1 vs Theorem 1} ?
    
    \item \textcolor{blue}{MIQ usually does not achieve uniform edges in complex models.}
        In Section 5, remove the claim that MIQ will generate uniform edge
        lengths. This is in general not true: The method will try to generate
        uniform edges but it usually does not achieve it in complex models.
    \end{itemize}

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